Repe ses les ?deps]6994356 p cleDOMA Ho e 1, patient Search . R Hw New Manay.. W
ID: 3312035 • Letter: R
Question
Repe ses les ?deps]6994356 p cleDOMA Ho e 1, patient Search . R Hw New Manay.. Week 13: Chap X Support of Background Checks by Political Party: In April of 2013, the U.S. Senate did not pass a bill to expand background checks to all gun sales despite popular approval of the idea. Gallup conducted a poll on this issue with the question: Would you vote for or against a law to require background checks for all gun sales?. The results by political affiliation are summarized in the contingency table below Observed Frequencies: Os Democrat Totals 278 74 352 For Checks 670 130 8OD The Test: Test for a dependent relationship between party affiliation and opinion on expanded background checks. Conduct this test at the 0.01 significance level. 331 45 376 Against Checks Totals 72 (a) What is the null hypothesis for this test? He: Party affiliation and opinion on expanded background checks are dependent variables. O He: Party affiliation and opinion on expanded backgro nd checks are independent variables. (b) What is the value of the test statistic? Round to 3 decimal places unless your software automatically rounds to 2 decimal places the value of the test statistic? Round to 3 decimal places unless your software automatically rounds to 2 decimal places. ()Use software to get the Pivalue of the test statistic. Round to 4 decimal places unless your software automatically rounds to 3 decimal places. P-value (d) what is the conclusion regarding the null hypothesis? O relect Ho Q tail to reject Ho (e) Choose the appropriate concluding stätement. Q We have proven that opinion on expanded background checks and party affiliation are independent. The evidence suggests that there is a dependent relationship between party affilation and opinion on expanded background checks. D There is not enough evidence to conclude that party affilation and opinion on expanded background checks are dependent. Additional Materials eBookExplanation / Answer
(a)
H0: Party affiliation and opinion on expanded background checks are independent variables.
(b)
DF = (r - 1) * (c - 1) = (2 - 1) * (3 - 1) = 2
Er,c = (nr * nc) / n
E1,1 = (670 * 352) / 800 = 294.8
E1,2 = (670 * 72) / 800 = 60.3
E1,3 = (670 * 376) / 800 = 314.9
E2,1 = (130 * 352) / 800 = 57.2
E2,2 = (130 * 72) / 800 = 11.7
E2,3 = (130 * 376) / 800 = 61.1
2 = [ (Or,c - Er,c)2 / Er,c ]
2 = (278 - 294.8)2/294.8 + (61 - 60.3)2/60.3 + (331 - 314.9)2/314.9
+ (74 - 57.2)2/57.2 + (11 - 11.7)2/11.7 + (45 - 61.1)2/61.1
= 11.01
(c)
P-value = P(2 > 11.01) = 0.0041 (for Degree of freedom = 2)
(d)
As, P-value is less than the significance level 0.01, we reject H0.
(e)
The evidence suggests that there is a dependent relationship between party affiliation and opinion on expanded ground checks.